POST UTME ABU 2020 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
Find the area under the curve \( y = x^2 \) from \( x = 0 \) to \( x = 4 \) u\sing integration.
A. 64
B. 80
C. 96
D. 112
Question 2
A probability experiment consists of two indep\endent events $A$ and $B$. If $P(A) = 0.4$ and $P(B) = 0.6$, find the value of $P(A cap B)$.
A. 0.2
B. 0.4
C. 0.6
D. 0.8
Question 3
Solve the system of equations $\begin{cases} x + y = 2 \ x - 2y = -3 \end{cases}$.
A. x = 1, y = 1
B. x = -1, y = 3
C. x = 1, y = 3
D. x = -1, y = 1
Question 4
A binary operation $ast$ is defined as $x ast y = xy + 1$. Find the value of $2 ast 3$.
A. 7
B. 8
C. 9
D. 10
Question 5
In the complex plane, let $z_1 = 2 + 3i$ and $z_2 = 4 - 5i$. Find the value of $|z_1 + z_2| + |z_1 - z_2|$.
A. 10
B. 15
C. 20
D. 25
Question 6
A binary number is represented as \( 1010_2 \). What is the decimal equivalent of this number?
A. 10
B. 11
C. 12
D. 13
Question 7
In the diagram below, the matrix A is given by \( A = egin{bmatrix} 2 & 1 \ 4 & 3 \end{bmatrix} \). Find the value of \( det\( A^2 \ \) ).
A. 25
B. 30
C. 35
D. 40
Question 8
Find the vector projection of the vector b = 2i + 3j onto the vector a = i + 2j.
A. 1/3 i + 2/3 j
B. 2/3 i + 1/3 j
C. 1/2 i + 1/2 j
D. 1/4 i + 3/4 j
Question 9
Find the area of the triangle with vertices $(0, 0)$, $(3, 0)$, and $(0, 2)$.
A. 6
B. 8
C. 10
D. 12
Question 10
Find the area under the curve \( y = \sin^2 x \) from \( x = 0 \) to \( x = \frac{pi}{2} \).
A. \( \frac{1}{2} \)
B. \( \frac{1}{4} \)
C. \( \frac{1}{3} \)
D. \( \frac{1}{6} \)
Question 11
Find the volume of the solid formed by revolving the region bounded by the curve $y = \frac{1}{2}x^2 - 2x + 3$, the $x$-axis, and the line $x = 1$ about the $x$-axis.
A. \frac{\pi}{6}
B. \frac{\pi}{3}
C. \frac{\pi}{2}
D. \frac{\pi}{4}
Question 12
If ( f(x) = \frac{1}{x^2 + 1} ), find the value of \( \int_{-1}^{1} f\( x \ \) \, dx ).
A. 0
B. \frac{\pi}{2}
C. \frac{\pi}{4}
D. \frac{\pi}{6}
Question 13
A die is rolled three times. What is the probability that the sum of the three rolls is 9?
A. \frac{1}{8}
B. \frac{1}{6}
C. \frac{1}{4}
D. \frac{1}{2}
Question 14
A histogram is constructed from the following data: 2, 4, 5, 6, 8, 9, 11, 12, 14, 16. What is the mean of the data set?
A. 7.5
B. 8.5
C. 9.5
D. 10.5
Question 15
A cylindrical \tank with a radius of 7m and a height of 10m is filled with water. What is the volume of water in the \tank, in cubic meters?
A. 700\pi
B. 700\pi + 100\pi
C. 700\pi - 100\pi
D. 100\pi

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